Here's a different perspective: if the government is involved in paying for your healthcare, that gives voters a say in how you live your life. Taking too many risks? Like wine or soft drinks a bit too much? Maybe you enjoy rock climbing, or horse riding, or skiing, or some other dangerous activity? Well, maybe I don't want to pay for your risks, and I get to call you a drunk, fat and lazy, or foolhardy and reckless, needing more regulation and laws to keep you in your place - and your health costs low. We'll ban tasty food, nice drinks, and any activities that are more than a standard deviation or two out of the normal risk profile. We'll have a nice gentle bland life mapped out for you with low health costs.
IMO the biggest elephant in the room is rationing. We can't give infinite healthcare to everybody for all their lives, particularly in very old age. We need to make hard trade-offs. In a free market system, the rationing is done by affordability and price levels: we choose who's more worthy of living longer by how much capital they've accumulated. In a more centralized system, we might choose to pay for interventions based on how much extra "life" they give, and ration by selecting a threshold for how much we pay for extra life year - this is how the UK NHS works, where life year is a QALY, quality-adjusted life year. But anything that doesn't address this elephant in the room, and appeals to emotions about the poor, sick, elderly, dying because they can't afford the treatment they need without considering who exactly we're going to leave to die and why, because we can't all be each other's caregivers for life, is intellectually bankrupt.